Uniformly perfect sets, rational semigroups, Kleinian groups and IFS's

摘要

We show that the Julia set of a non-elementary rational semigroup G isuniformly perfect when there is a uniform bound on the Lipschitz constants ofthe generators of G. This also proves that the limit set of a non-elementaryMoebius group is uniformly perfect when there is a uniform bound on theLipschitz constants of the generators of the group and this implies that thelimit set of a finitely generated non-elementary Kleinian group is uniformlyperfect.